This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A133129 #20 Jul 03 2023 08:43:58 %S A133129 1,8,50,322,2066,13262,85126,546410,3507314,22512862,144506294, %T A133129 927561722,5953863490,38216853518,245307588134,1574588362378, %U A133129 10107019231634,64875265300670,416423472774166,2672952594083738,17157235452223586,110129423550044398 %N A133129 Number of black/white colorings of a 3 X n rectangle which have no monochromatic 2 by 2 subsquares. %H A133129 Alois P. Heinz, <a href="/A133129/b133129.txt">Table of n, a(n) for n = 0..1000</a> %H A133129 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6, 3, -2). %F A133129 G.f.: 1+x*(8+2*x-2*x^2)/(1-6*x-3*x^2+2*x^3). - _Colin Barker_, Jan 04 2012 %e A133129 a(2) = 50 because if the middle row is not monochromatic, the top and bottom rows are unconstrained, contributing 2*4*4. if the middle row is monochromatic, the top and bottom rows can each take on only 3 values contributing 2*3*3. %Y A133129 Cf. A055099, A133357. %Y A133129 Column k=3 of A181245. %K A133129 nonn %O A133129 0,2 %A A133129 _Victor S. Miller_, Sep 19 2007 %E A133129 More terms from _Colin Barker_, Jan 03 2012 %E A133129 a(0)=1 prepended and g.f. adapted by _Alois P. Heinz_, Feb 19 2015